Abstract
We study a class of fractional predator-prey systems with Holling II functional response. A unique positive solution of this system is obtained. In order to prove the asymptotical stability of positive equilibrium for this system, we study the Lyapunov stability theory of a fractional system.
Highlights
We consider the following fractional predator-prey model with Holling Type II functional response: dαx (t) = x (t) (a −bx γy (t) + βx (t) ) dtα, (1) dαy y
We briefly review the main notions and results from the recent fractional calculus proposed by Jumarie [12, 18, 19]
= ∞, words, to complete the proof all we need to show is that τ∞ = ∞
Summary
We consider the following fractional predator-prey model with Holling Type II functional response: dαx (t). One of the most popular predatorprey models with Holling Type II functional response is established in [1, 2]. The asymptotic behavior of a stochastic predator-prey system with Holling Type II functional response is studied in [3]. White noise is always present in natural world; Liu et al studied the asymptotic behavior of a stochastic predator-prey system with Holling II functional response. We present a fractional prey-predator model (1) to describe the ecosystem which performs well in the practical problem.
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